PDETime: Rethinking Long-term Multivariate Time Series Forecasting from the Perspective of Partial Differential Equations

Shiyi Qi, Zenglin Xu, Yiduo Li, Liangjian Wen, Qingsong Wen, Qifan Wang, Yuan Qi

Keywords: long-term multivariate time series forecasting

Abstract:

Recent advancements in deep learning have led to the development of various approaches for long-term multivariate time-series forecasting (LMTF). Most of these approaches can be categorized as either historical-value-based methods, which rely on discretely sampled past observations, or time-index-based methods that model time indices directly as input variables. However, real-world dynamical systems often exhibit nonstationarity and suffer from insufficient sampling frequency, posing challenges such as spurious correlations between time steps and difficulties in modeling complex temporal dependencies.
In this paper, we treat multivariate time series as data sampled from a continuous dynamical system governed by partial differential equations (PDEs) and propose a new model called PDETime.
Instead of predicting future values directly, PDETime employs an encoding-integration-decoding architecture: it predicts the partial derivative of the system with respect to time (i.e., the first-order difference) in the latent space and then integrates this information to forecast future series. This approach enhances both performance and stability, especially in scenarios with extremely long forecasting windows. Extensive experiments on seven diverse real-world LMTF datasets demonstrate that PDETime not only adapts effectively to the intrinsic spatiotemporal nature of the data but also sets new benchmarks by achieving state-of-the-art results.

Primary Area: applications to computer vision, audio, language, and other modalities

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Submission Number: 14134